First direct probe of strong nuclear force

Extended Data Fig. 1 SRC pair breakup.

Diagrammatic representation and four-momentum kinematics of the two-nucleon knockout A( e ,  e ′ Np ) reaction within the SRC model. The dashed red lines represent off-shell particles and solid black lines represent detected particles. The A −2 system is undetected.

Extended Data Fig. 2 Kinematical distributions and A( e ,  e ′ pp )/A( e ,  e ′ p ) ratios for A  = 12–208 nuclei.

a – c , Comparison of the number of A( e ,  e ′ p ) event reactions versus the ( e ,  e ′ p ) missing momentum p _miss ( a ), Q ² ( b ) and x _B ( c ). d – f , Comparison of the number of A( e ,  e ′ pp ) event reactions versus the ( e ,  e ′ p ) missing momentum p _miss ( d ), Q ² ( e ) and x _B ( f ). The total number of counts in aluminium (cyan), iron (orange), and lead (purple) was scaled to match that of carbon (dark blue). The shaded bands indicate the 1 σ statistical uncertainty of the data.

Extended Data Fig. 3 Momentum-transfer and missing-momentum angular correlations.

a – d , Distribution of the relative angle between the momentum transfer q and the ( e ,  e ′ p ) missing momentum for A( e ,  e ′ p ) ( a , b ) and A( e ,  e ′ pp ) ( c , d ). The panels at left compare the ¹² C data and GCF calculations using different NN interaction models ( a , c ); and the panels at right compare the data for carbon (blue), aluminium (cyan), iron (orange), and lead (purple) nuclei ( b , d ). The total number of counts in the aluminium, iron and lead data has been scaled to match that of carbon. In a and c , the width of the band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1 σ confidence level. The shaded bands in b and d indicate the 1 σ statistical uncertainty of the data.

Extended Data Fig. 4 Electron and proton kinematics.

Momentum and angle distributions of scattered electrons and protons for ¹² C( e ,  e ′ p ) ( a , c , e , h ) and ¹² C( e ,  e ′ pp ) ( b , d , f , g , i , j ) events. Coloured bands show the various GCF calculations. The width of the shaded band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1 σ confidence level.

Extended Data Fig. 5 Kinematic correlations of ¹² C( e ,  e ′ p ) events.

a , Q ² versus the missing-momentum distribution of ¹² C( e ,  e ′ p ) data. Owing to the event selection criteria, as p _miss approaches 1 GeV/ c , the minimum Q ² of the data approaches 3 GeV/ c . b , E _miss versus p _miss of the ¹² C( e ,  e ′ p ) data. The red line indicates the expected E _miss – p _miss correlation for the breakup of a stationary pair.

Extended Data Fig. 6 Universal functions for pp and np pairs and the momentum dependence of their ratio.

The relative momentum distributions for different NN interaction models studied in this work, for pn ( a ) and pp ( b ). c , The momentum dependence of the fraction of protons belonging to pp SRC pairs in ¹² C.

Extended Data Fig. 7 Light-cone calculations of the nuclear spectral function and momentum fractions.

a – j , As in Fig.3a–j. k , l , The reconstructed initial light-cone momentum fraction carried by the struck nucleon for ( e ,  e ′ p ) ( k ) and ( e ,  e ′ pp ) ( l ) events. m , The total pair light-cone momentum fraction for ( e ,  e ′ pp ) events. The data points are identical to those in Fig. 3a–j. The bands are different and show the results of the GCF calculations using light-cone formalism and various NN interaction models. The width of the shaded band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1 σ confidence level.

Extended Data Fig. 8 Scale dependence and non-local interactions.

a – c , As in Fig.3a, b ( a , b ) and Fig.2a ( c ), but also including the non-local N3LO (600 MeV/ c ) interaction. The width of the shaded band and the data error bars show the model systematic uncertainties and data statistical uncertainties, respectively, each at the 1 σ confidence level. See Methods for details.